Question

How do you simplify numbers using the imaginary unit (i)? Ex: sqrt -16

Answer 1

If you have something in the form \(\sqrt{-a}\) for some \(a > 0\), then we can break it up using exponent / radical properties:
\(\sqrt{-a} = \sqrt{-1 \times a} = \sqrt{-1} \sqrt{a} = i \sqrt{a} \)

Answer 2

so it would be i\[\sqrt{16}\]?

Answer 3

\(i \sqrt{16}\) Yes, although we can go a step further since \(\sqrt{16}\) is the square root of a perfect square.
= \(4i\)

Answer 4

Okay thanks.

Answer 5

You're welcome. :)